BGonline.org Forums

Any reason to roll out multiple-of-36 games?

Posted By: Timothy Chow
Date: Wednesday, 30 September 2009, at 1:55 a.m.

In Response To: Any reason to roll out multiple-of-36 games? (Bob Koca)

Bob, I'm not convinced by your argument. The motivation behind stratified sampling, or quasirandom dice I guess I should say, is the notion that dice sequences that start with the same roll are correlated. In Protocol A, the two X's that correspond to the same roll are correlated and can't be treated as independent. Another way to put it is that if Q is the equity (after the doubling decision) and Q₁₁, Q₁₂, etc., are the equities after rolling the dice, then Q = Q₁₁ + 2Q₁₂ + 2Q₁₃ + ... + Q₆₆, and the two X's corresponding to (say) Q₁₂ are really two independent samples of Q₁₂ and are therefore correlated more with each other than with a sample of (say) Q₁₁.

Here's another way to look at it. Let's take 3-sided dice instead of 6-sided dice for simplicity. Then there are 6 possible rolls, three of which occur twice as often as the others. Suppose I have the resources to take 36 samples. Am I better off sampling each of the 6x6 possible pairs of rolls once, or am I better off taking 8 samples of each of the non-doubles and 4 samples each of the doubles? It's not clear. On the one hand, the non-doubles matter more so it might seem we should sample them proportionately heavily. However, perhaps the volatility is so large that I had better make sure I take at least one sample of each of the 6x6 possible pairs of rolls. I don't think we can say for sure which way is better.

In particular, I now think I overstated the case when I said that multiples of 21 would make more sense than multiples of 36. Either way could work out better and it's hard to know which.

Messages In This Thread

• Any reason to roll out multiple-of-36 games?
  Timothy Chow -- Monday, 28 September 2009, at 5:01 p.m.
  • Any reason to roll out multiple-of-36 games?
    Gregg Cattanach -- Monday, 28 September 2009, at 5:27 p.m.
    • Any reason to roll out multiple-of-36 games?
      Michael Petch -- Monday, 28 September 2009, at 5:38 p.m.
  • Any reason to roll out multiple-of-36 games?
    Frank Berger -- Monday, 28 September 2009, at 5:58 p.m.
    • Any reason to roll out multiple-of-36 games?
      Rich Munitz -- Monday, 28 September 2009, at 6:47 p.m.
      • Any reason to roll out multiple-of-36 games?
        Bob Koca -- Monday, 28 September 2009, at 7:27 p.m.
        • Any reason to roll out multiple-of-36 games?
          Maik Stiebler -- Monday, 28 September 2009, at 9:32 p.m.
        • Any reason to roll out multiple-of-36 games?
          Timothy Chow -- Wednesday, 30 September 2009, at 1:55 a.m.
          • Any reason to roll out multiple-of-36 games?
            Bob Koca -- Wednesday, 30 September 2009, at 2:44 a.m.
            • Any reason to roll out multiple-of-36 games?
              Maik Stiebler -- Wednesday, 30 September 2009, at 11:17 a.m.
          • Any reason to roll out multiple-of-36 games?
            Maik Stiebler -- Wednesday, 30 September 2009, at 11:25 a.m.
  • Any reason to roll out multiple-of-36 games?
    Jason Lee -- Monday, 28 September 2009, at 7:29 p.m.
    • Any reason to roll out multiple-of-36 games?
      Maik Stiebler -- Monday, 28 September 2009, at 9:13 p.m.
    • Any reason to roll out multiple-of-36 games?
      Ian Shaw -- Monday, 28 September 2009, at 9:33 p.m.